Formulae

1

Mechanical

𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 =𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑡𝑖𝑚𝑒

𝑣 =𝑥

𝑡

𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛

𝑣 =∆𝑠

∆𝑡

𝑠𝑝𝑒𝑒𝑑 =𝑑

𝑡

𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛

𝑎 =∆𝑣

∆𝑡

𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ

Equations of motion

𝑣 = 𝑢 + 𝑎𝑡

𝑠 =1

2(𝑢 + 𝑣)𝑡

𝑠 = 𝑢𝑡 +1

2𝑎𝑡2

𝑣2 = 𝑢2 + 2𝑎𝑠

Projectile

Vertical :

Time for maximum height, t

Formulae

2

𝑡 =𝑢 sin 𝜃

𝑔

Instantaneous height, y

𝑦 = (𝑢 sin 𝜃) 𝑡 −1

2𝑔𝑡

Total time taken, T

𝑇 =2𝑢 sin 𝜃

𝑔

Horizontal :

Instantaneous displacement, x

𝑥 = (𝑢 cos 𝜃) 𝑡

Range, R

𝑅 =𝑢2 sin 2𝜃

𝑔

Newton’s Second Law of Motion

𝐹 = 𝑚𝑎

Weight

𝑊 = 𝑚𝑔

Moment=force x distance from pivot

𝑚𝑜𝑚𝑒𝑛𝑡 = 𝐹 × 𝑥1

Moment of anti-clockwise=Moment of clockwise

Work done

𝑊 = 𝐹 × 𝑠

𝑊 = 𝐹𝑠 cos 𝜃

Gravitational Potential Energy

Formulae

3

𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑔. 𝑝. 𝑒 = 𝑤𝑒𝑖𝑔ℎ𝑡 × 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 ℎ𝑒𝑖𝑔ℎ𝑡

𝐸𝑝 = 𝑚𝑔ℎ

Kinetic Energy

𝐾𝑖𝑛𝑒𝑡𝑖𝑐 𝐸𝑛𝑒𝑟𝑔𝑦 =1

2× 𝑚𝑎𝑠𝑠 × 𝑠𝑝𝑒𝑒𝑑2

𝐸𝑘 =1

2𝑚𝑣2

GPE –KE Transformation

𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝑔. 𝑝. 𝑒 = 𝑔𝑎𝑖𝑛 𝑖𝑛 𝑘. 𝑒

Efficiency

𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑢𝑠𝑒𝑓𝑢𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦

𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦× 100%

Power

𝑝𝑜𝑤𝑒𝑟 =𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒

𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛

𝑃 =𝑊

𝑡

𝑝𝑜𝑤𝑒𝑟 = 𝑓𝑜𝑟𝑐𝑒 × 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

𝑃 = 𝐹 × 𝑣

Linear momentum

𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 = 𝑚𝑎𝑠𝑠 × 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

𝑝 = 𝑚𝑣

In a closed system:

total momentum of object before collision=total momentum of object after collision

𝑚𝐴𝑢𝐴 + 𝑚𝐵𝑢𝐵 = 𝑚𝐴𝑣𝐴 + 𝑚𝐵𝑣𝐵

Relative velocity

𝑣𝐵 − 𝑣𝐴 = −(𝑢𝐵 − 𝑢𝐴)

Change in momentum

Formulae

4

∆𝑝 = 𝑝𝑓 − 𝑝𝑖

Impulse

∆𝑝 = 𝐹 × ∆𝑡

Density

𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =𝑚𝑎𝑠𝑠

𝑣𝑜𝑙𝑢𝑚𝑒

𝜌 =𝑚

𝑉

Pressure

𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =𝑛𝑜𝑟𝑚𝑎𝑙 𝑓𝑜𝑟𝑐𝑒

𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎

𝑝 =𝐹

𝐴

Pressure in a fluid

𝑝 = 𝜌𝑔ℎ

Force constant

𝑘 =𝐹

𝑥

Strain

𝑠𝑡𝑟𝑎𝑖𝑛 =𝑒𝑥𝑡𝑒𝑛𝑠𝑖𝑜𝑛

𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ

𝑠𝑡𝑟𝑎𝑖𝑛 =𝑥

𝐿

Stress

𝑠𝑡𝑟𝑒𝑠𝑠 =𝑓𝑜𝑟𝑐𝑒

𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎

Formulae

5

𝑠𝑡𝑟𝑒𝑠𝑠 =𝐹

𝐴

Young modulus

𝑌𝑜𝑢𝑛𝑔 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 = 𝑠𝑡𝑟𝑒𝑠𝑠

𝑠𝑡𝑟𝑎𝑖𝑛

𝐸 =𝜎

𝜀

Elastic potential energy

𝐸 =1

2𝐹𝑥

𝐸 =1

2𝑘𝑥2

Electric field strength

𝐸 =𝐹

𝑄

𝐸 =𝑉

𝑑

Current

𝑐𝑢𝑟𝑟𝑒𝑛𝑡 =𝑐ℎ𝑎𝑟𝑔𝑒

𝑡𝑖𝑚𝑒

𝑐ℎ𝑎𝑟𝑔𝑒 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 × 𝑡𝑖𝑚𝑒

∆𝑄 = 𝐼∆𝑡

Resistance

𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 =𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒

𝑐𝑢𝑟𝑟𝑒𝑛𝑡

𝑅 =𝑉

𝐼

𝑉 = 𝐼𝑅

Electrical Power

𝑝𝑜𝑤𝑒𝑟 =𝑒𝑛𝑒𝑟𝑔𝑦 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑟𝑒𝑑

𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛

𝑃 =∆𝑊

∆𝑡

Formulae

6

∆𝑊 = 𝑉∆𝑄

𝑃 = 𝑉𝐼

Power and Resistance

𝑃 = 𝐼2𝑅

𝑃 =𝑉2

𝑅

Calculating energy

𝑝𝑜𝑤𝑒𝑟 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 × 𝑣𝑜𝑙𝑡𝑎𝑔𝑒

𝑒𝑛𝑒𝑟𝑔𝑦 = 𝑝𝑜𝑤𝑒𝑟 × 𝑡𝑖𝑚𝑒

𝑒𝑛𝑒𝑟𝑔𝑦 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑟𝑒𝑑 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 × 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 × 𝑡𝑖𝑚𝑒

∆𝑊 = 𝐼𝑉∆𝑡

Kirchhoff’s 1st Law

𝛴Iin=𝛴Iout

Kirchhoff’s 2nd

Law

𝛴E=𝛴V

Resistors in series

𝑅 = 𝑅1 + 𝑅2 + 𝑅3 … ..

Resistors in parallel

1

𝑅=

1

𝑅1+

1

𝑅2+

1

𝑅3+ ⋯

V-I Graph

𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 =1

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑜𝑓 𝑔𝑟𝑎𝑝ℎ

Resistivity

𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 = 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ×𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎

𝑙𝑒𝑛𝑔𝑡ℎ

Formulae

7

𝜌 =𝑅𝐴

𝐿

Internal resistance

𝐸 = 𝐼(𝑅 + 𝑟)

Potential dividers

𝑉𝑜𝑢𝑡 = ⌊𝑅2

𝑅1 + 𝑅2⌋ × 𝑉𝑖𝑛

Frequency

𝑓 =1

𝑇

Period

𝑇 =1

𝑓

Intensity

𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 =𝑝𝑜𝑤𝑒𝑟

𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎

Intensity and amplitude

𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦

𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒2= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

Wave speed

𝑣 = 𝑓 × 𝜆

Speed of light

𝑐 = 𝑓𝜆

Destructive interference

𝑝𝑎𝑡ℎ 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =1

2𝜆, 1

1

2𝜆, 2

1

2𝜆, … ..

𝑝𝑎𝑡ℎ 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = (𝑛 +1

2)𝜆

Constructive interference

𝑝𝑎𝑡ℎ 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 0, 𝜆, 2𝜆, 3𝜆 ….

Formulae

8

𝑝𝑎𝑡ℎ 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑛𝜆

Young Double-slit

𝜆 =𝑎𝑥

𝐷

a=slit separation

x=fringe separation

D=slit-to-screen distance

Determining 𝜆 with a grating

𝑑 sin 𝜃 = 𝑛𝜆

Air column (Open ends)

Formulae

9

𝐿 =𝑛𝜆

2

𝑓 =𝑛𝑣

2𝐿

Air column (Close ends)

Formulae

10

Error

𝜆 = 2(𝑙2 − 𝑙1)

Sting

Formulae

11

Air Closed

Air open

Formulae

12

Radioactivity

α-decay

𝐴𝑍

𝑋 →𝐴 − 4𝑍 − 2

𝑌 +42

∝

β-decay

10

𝑛 →11

𝑝 +0

−1𝑒 + 𝑒𝑛𝑒𝑟𝑔𝑦

γ-emission